Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Multivariate Process Capability Index Using Inverted Normal Loss Function

역정규 손실함수를 이용한 다변량 공정능력지수

  • Moon, Hye-Jin (Department of Industrial and Management Engineering, Incheon National University) ;
  • Chung, Young-Bae (Department of Industrial and Management Engineering, Incheon National University)
  • 문혜진 (인천대학교 산업경영공학과) ;
  • 정영배 (인천대학교 산업경영공학과)
  • Received : 2018.05.16
  • Accepted : 2018.06.28
  • Published : 2018.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

In the industrial fields, the process capability index has been using to evaluate the variation of quality in the process. The traditional process capability indices such as $C_p$, $C_{pk}$, $C_{pm}$ and $C^+_{pm}$ have been applied in the industrial fields. These traditional process capability indices are mainly applied in the univariate analysis. However, the main streams in the recent industry are the multivariate manufacturing process and the multiple quality characteristics are corrected each other. Therefore, the multivariate statistical method should be used in the process capability analysis. The multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. Hence, the purpose of the study is to develop a more effective multivariate process index ($MC_{pI}$) using the multivariate inverted normal loss function. The multivariate inverted normal loss function has the flexibility for the any type of the symmetrical and asymmetrical loss functions as well as the economic information. Especially, the proposed modeling method for the multivariate inverted normal loss function (MINLF) and the expected loss from MINLF in this paper can be applied to the any type of the symmetrical and asymmetrical loss functions. And this modeling method can be easily expanded from a bivariate case to a multivariate case.

Keywords

References

  1. Boyles, R.A., The Taguchi Capability index, Journal of Quality Technology, 1991, Vol. 23, No. 1, pp. 17-26. https://doi.org/10.1080/00224065.1991.11979279
  2. Chan, L.K., Chung, S.W., and Spiring, F.A., A New Measure of Process Capability : Cpm, Journal of Quality Technology, 1988, Vol. 20, No. 3, pp. 162-175. https://doi.org/10.1080/00224065.1988.11979102
  3. Chung, Y.B. and Kim, Y.S., Comparison and Application of Process Capability indices, Journal of Society of Korea Industrial and Systems Engineering, 2007, Vol. 30, No. 4, pp. 182-189.
  4. Chung, Y.B. and Mun, H.J., A Study on Process Capability Index using Reflected Normal Loss Function, Journal of The Korean Society for Quality Management, 2002, Vol. 30, No. 3, pp. 66-78.
  5. Chung, Y.B., A Multivariate Process Capability Index using Expected Loss, Journal of Society of Korea Industrial and Systems Engineering, 2005, Vol. 28, No. 4, pp. 116-123.
  6. Drain, D. and Gough, A.M., Applications of the Upside-Down Normal Loss, IEEE Transactions on Semiconductor Manufacturing, 1996, Vol. 9, No. 1, pp. 143-145. https://doi.org/10.1109/66.484295
  7. Hashemi, S.J., Ahmed, S., and Khan, F., Operational loss modeling for process facilities using multivariate loss functions, Chemical Engineering Research and Design, 2015, Vol. 104, pp. 333-345. https://doi.org/10.1016/j.cherd.2015.08.019
  8. Khan, F., Wang, H., and Yang, M., Application of loss functions in process economic risk assessment, Chemical Engineering Research and Design, 2016, Vol. 111, pp. 371-386. https://doi.org/10.1016/j.cherd.2016.05.022
  9. Leung, B.P.K. and Spiring, F.A., Some Properties of the Family of Inverted Probability Loss Functions, Quality Technology & Quantitative Management, 2004, Vol. 1, No. 1, pp. 125-147. https://doi.org/10.1080/16843703.2004.11673068
  10. Mun, H.J. and Chung, Y.B., A Study on Multivariate Process Capability Index using Quality Loss Function, Journal of Society of Korea Industrial and Systems Engineering, 2002, Vol. 25, No. 2, pp. 1-10.
  11. Shahriari, H., Hubele, N.F., and Lawrence, F.P., A multivariate process capability vector, Proceeding of the 4th Industrial Engineering Research Conference, Institute of Industrial Engineers, 1995, pp. 304-309
  12. Spiring, F.A. and Yeung, A.S., A General Class of Loss Functions with Industrial Applications, Journal of Quality Technology, 1998, Vol. 30, No. 2, pp. 152-162. https://doi.org/10.1080/00224065.1998.11979834
  13. Spiring, F.A., The Reflected Normal Loss Function, Canadian Journal of Statistics, 1993, Vol. 21, pp. 321-330. https://doi.org/10.2307/3315758
  14. Taam, W., Subbaiah, P., and Liddy, J.W., A Note on Multivariate Capability Indices, Journal of Applied Statistics, 1993, Vol. 20, pp. 339-351. https://doi.org/10.1080/02664769300000035

Cited by

  1. Analysis of Multivariate Process Capability Using Box-Cox Transformation vol.42, pp.2, 2018, https://doi.org/10.11627/jkise.2019.42.2.018